We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete Cspectral set for an operator T , then it is a complete M -numerical radius set, where M = 12 (C + C −1). In particular, in view of Crouzeix’s theorem, there is...

We show that only the segment borders have to be taken into account as cut point candidates in searching for the optimal multisplit of a numerical value rangewith respect to convex attribute evaluation functions. Segment borders can be found efficiently in a linear-time preprocessing step. For strictly convex evaluation functions inspecting all segment borders is also necessary. With Training S...

Histogram equalization, which stretches the dynamic range of intensity, is the most common method for enhancing the contrast of image. Contrast Limited Adaptive Histogram Equalization (CLAHE), proposed by K. Zuierveld, has two key parameters: block size and clip limit. These parameters are mainly used to control image quality, but have been heuristically determined by users. In this paper, we p...

For an $$n\times n$$ complex matrix C, the C-numerical range of a bounded linear operator T acting on Hilbert space dimension at least n is set numbers $$\textrm{tr}\,(CX\,^*\,TX)$$ , where X partial isometry satisfying $$X^*X = I_n$$ . It shown that $$\begin{aligned} \textbf{cl}(W_C(T)) \cap \{\textbf{cl}(W_C(U)): U \hbox { unitary dilation } T\} \end{aligned}$$ for any contraction if and only...